1. The cohomology annihilator of a curve singularity.
- Author
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Esentepe, Özgür
- Subjects
- *
GORENSTEIN rings , *TRIANGULATED categories , *ALGEBRAIC curves , *LOCAL rings (Algebra) , *COMMUTATIVE rings , *COHOMOLOGY theory - Abstract
The aim of this paper is to study the theory of cohomology annihilators over commutative Gorenstein rings. We adopt a triangulated category point of view and study the annihilation of stable category of maximal Cohen-Macaulay modules. We prove that in dimension one the cohomology annihilator ideal and the conductor ideal coincide under mild assumptions. We present a condition on a ring homomorphism between Gorenstein rings which allows us to carry the cohomology annihilator of the domain to that of the codomain. As an application, we generalize the Milnor-Jung formula for algebraic curves to their double branched covers. We also show that the cohomology annihilator of a Gorenstein local ring is contained in the cohomology annihilator of its Henselization and in dimension one the cohomology annihilator of its completion. Finally, we investigate a relation between the cohomology annihilator of a Gorenstein ring and stable annihilators of its noncommutative resolutions. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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